Optical data communication typically involves modulating the amplitude and wavelength of a beam of laser light, and detecting that modulation downstream. The present invention is directed to a complementary approach to conveying information on a beam of light based on the properties of helical optical modes.
A helical mode is characterized by the corkscrew-like topology of its wave fronts, which can be described by a real-valued phase function:φ({right arrow over (ρ)})=lθ,  (1)where {right arrow over (ρ)}=(ρ, θ) is the position in a plane transverse to the beam's axis, with θ being the polar angle, and l is an integral winding number known as the topological charge that describes the pitch of the helix. This phase establishes the beam's topology through the general expression for the magnitude of the electric field in a collimated beam,El({right arrow over (ρ)})=υl({right arrow over (ρ)})exp(iφ({right arrow over (ρ)}))exp(iφl),  (2)where υl({right arrow over (ρ)}) is the real-valued amplitude profile and φl is an arbitrary constant phase. A general superposition of helical modes can be written as
                              E          ⁡                      (                          ρ              →                        )                          =                              ∑                          l              =                              -                ∞                                      ∞                    ⁢                                                    E                l                            ⁡                              (                                  ρ                  →                                )                                      .                                              (        3        )            
If it is assumed that all the beams in the superposition have the same amplitude profile, υ({right arrow over (ρ)}) perhaps with different amplitudes, αl, then
                                          E            ⁡                          (                              ρ                →                            )                                =                                    ∑                              l                =                                  -                  ∞                                            ∞                        ⁢                                          α                l                            ⁢                              υ                ⁡                                  (                                      ρ                    →                                    )                                            ⁢                              exp                ⁡                                  (                                      ⅈ                    ⁢                                                                                  ⁢                                          φ                      ⁡                                              (                                                  ρ                          →                                                )                                                                              )                                            ⁢                              exp                ⁡                                  (                                      ⅈ                    ⁢                                                                                  ⁢                                          ϕ                      l                                                        )                                                                    ,                            (        4        )            with normalization
            ∑              l        =                  -          ∞                    ∞        ⁢                                    α          l                            2        =  1.For the practical applications, only a limited set of the αl will be non-zero.